TY - JOUR
AU - Mehran, S.
AU - Namdari, M.
AU - Soltanpour, S.
PY - 2018/10/04
Y2 - 2024/06/18
TI - On the essentiality and primeness of λ-super socle of C(X)
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 19
IS - 2
SE -
DO - 10.4995/agt.2018.9058
UR - https://ojs.upv.es/index.php/AGT/article/view/9058
SP - 261-268
AB - <p>Spaces X for which the annihilator of Sλ(X), the λ-super socle of C(X) (i.e., the set of elements of C(X) that cardinality of their cozerosets are less than λ, where λ is a regular cardinal number such that λ≤|X|) is generated by an idempotent are characterized. This enables us to find a topological property equivalent to essentiality of Sλ(X). It is proved that every prime ideal in C(X) containing Sλ(X) is essential and it is an intersection of free prime ideals. Primeness of Sλ(X) is characterized via a fixed maximal ideal of C(X).</p>
ER -